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CLEP College Algebra Topics

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1Adding and Subtracting Integers

1.1Introduction to integer addition
1.2Adding integers
1.3Introduction to integer subtraction
1.4Subtracting integers
1.5Application of integer operations

2Multiplying and Dividing Integers

2.1Multiplying integers
2.2Dividing integers
2.3Order of operations (PEMADS)

3Primes and Common Factors

3.1Prime factorization
3.2Least Common Multiple (LCM) (free lessons)
3.3Greatest Common Factors (GCF)

4Fractions

4.1Adding fractions with like denominators
4.2Subtracting fractions with like denominators
4.3Adding and subtracting fractions with unlike denominators
4.4Multiplying proper fractions
4.5Dividing fractions and mixed numbers

5Decimals

5.1Adding and subtracting decimal numbers
5.2Multiplying decimal numbers
5.3Dividing decimal numbers
5.4Scientific notation
5.5Rational vs. Irrational numbers

6Expressions and Equations

6.1Patterns
6.2Adding and subtracting polynomials
6.3Multiplying polynomials by monomials
6.4Solving linear equations using multiplication and division (free lessons)
6.5Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
6.6Solving one - step equations: x+a=bx + a = b
6.7Solving linear equations with variables on both sides

7Introduction to Equations

7.1Evaluating algebraic expressions
7.2Solving literal equations
7.3Applications of polynomial functions
7.4Money related questions in linear equations (free lessons)

8Absolute Value and Equations

8.1Absolute value functions (free lessons)
8.2Solving absolute value equations
8.3Solving absolute value inequalities

9Graphing Inequalities

9.1Express linear inequalities graphically and algebraically (free lessons)
9.2Solving one-step linear inequalities (free lessons)
9.3Solving multi-step linear inequalities (free lessons)
9.4Graphing linear inequalities in two variables (free lessons)

10Linear Equations

10.1Word problems of graphing linear functions
10.2Rate of change
10.3Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
10.4General form: Ax + By + C = 0 (free lessons)
10.5Point-slope form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
10.6Parallel and perpendicular lines in linear functions (free lessons)

11Graphing Functions

11.1Domain and range of a function (free lessons)
11.2Identifying functions
11.3Function notation (free lessons)
11.4Graphing linear functions using x- and y-intercepts (free lessons)
11.5Determining number of solutions to linear equations (free lessons)
11.6Using elimination method to solve systems of equations
11.7Using substitution method to solve systems of equations
11.8Solving systems of linear equations by graphing

12Exponents and Multiplying Polynomials

12.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
12.2Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
12.3Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
12.4Combining the exponent rules
12.5Exponents: Zero exponent: a0=1 a^0 = 1
12.6Multiplying binomial by binomial (free lessons)
12.7Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)

13Factoring

13.1Common factors of polynomials (free lessons)
13.2Factor by taking out the greatest common factor (free lessons)
13.3Factoring polynomials: ax2+bx+cax^2 + bx + c
13.4Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)
13.5Factoring difference of squares: x2−y2x^2 - y^2
13.6Introduction to quadratic functions (free lessons)
13.7Factoring polynomials by grouping
13.8Factoring polynomials: x2+bx+cx^2 + bx + c (free lessons)
13.9Evaluating polynomials
13.10Word problems of polynomials

14Radical Expressions and Quadratic Equations

14.1Evaluating and simplifying radicals
14.2Converting radicals to mixed radicals

15Imaginary and Complex Numbers

15.1Introduction to imaginary numbers (free lessons)
15.2Adding and subtracting complex numbers
15.3Multiplying and dividing complex numbers
15.4Complex conjugates

16Solving Quadratic Equations

16.1Solving quadratic equations by factoring
16.2Solving quadratic equations by completing the square
16.3Solving quadratic equations using the quadratic formula
16.4Nature of roots of quadratic equations: The discriminant
16.5Applications of quadratic equations

17Ratio, Proportion, Area, and Perimeter

17.1Ratios (free lessons)
17.2Similar polygons

18Surface Area and Volume

18.1Surface area and volume of prisms (free lessons)
18.2Surface area and volume of pyramids
18.3Surface area and volume of cylinders
18.4Surface area and volume of cones (free lessons)
18.5Surface area and volume of spheres

19Probability and Statistics

19.1Median and mode
19.2Mean
19.3Application of averages
19.4Introduction to probability
19.5Organizing outcomes
19.6Probability of independent events
19.7Fundamental counting principle
19.8Combinations
19.9Permutations

20Coordinate Geometry

20.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
20.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
20.3Solving second degree trigonometric equations

21Negative and Rational Exponents

21.1Rational exponents
21.2Solving radical equations
21.3Basic radical functions

22Composite Functions and Inverses

22.1Composite functions (free lessons)
22.2Inverse functions (free lessons)

23Logarithms and Exponential Functions

23.1What is a logarithm?
23.2Evaluating logarithms without a calculator
23.3Product rule of logarithms (free lessons)
23.4Quotient rule of logarithms
23.5Combining product rule and quotient rule in logarithms
23.6Solving logarithmic equations (free lessons)
23.7Evaluating logarithms using change-of-base formula
23.8Exponential growth and decay by a factor
23.9Exponential decay: Half-life (free lessons)
23.10Natural log: ln
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